Preheat oven to 375 degrees F. In a large saucepan cook carrots and parsnips, covered, in a small amount of boiling water for minutes. Drain.
In a 13x9x2-inch baking pan combine the partially cooked carrots and parsnips and the beets. Sprinkle with parsley; marjoram, thyme, or rosemary; and salt. Drizzle with olive oil or cooking oil. Toss gently to coat vegetables. Cover the pan with foil.
Bake for 30 minutes, stirring vegetables once. Stir in squash pieces. Cover and bake about 20 minutes more or just until vegetables are barely done. Remove vegetables from oven.
Increase oven temperature to 450 degree F. Stir brown sugar into vegetables until thoroughly combined. Return vegetables to oven and bake, uncovered, for 15 to 20 minutes more or until vegetables are tender and glazed. Transfer to a serving dish. Makes 8 to 10 servings.